Very enlightening! Looks like we've found the issue. Here's a StackExchange discussion about it. The tl;dr is that it's likely malware or remnants of one. Please read the discussion for ideas on how to solve it, but here are my suggestions in order of preference.

Reformat PC. With Windows 10 recently released it's a great time to make the jump.

Try to repair your PC using Microsoft Security Essentials (reported to work in the discussion).

As a sidenote, it may be a good idea to first uninstall ALL Java versions you have installed on your computer via "Add or Remove Programs" in Windows and then install the latest (currently Java 8 x64 Update 60).

Thanks for your reply. I really want to get this bot working, one of my friends uses it and it looks great. Here is the screenshot. I'm assuming there's something on my computer blocking runemate, but I can't work out what it is.

try redownloaded java guy had similar problem last night that I helped redownload jdk and java then restart pc, if that doesn't work check your firewall

Click to expand...

Thanks for your reply.
I've updated my JDK and the RuneMate client, and now I'm getting some positive results. It's asking me to update my Java to the 64 bit variant so I'm doing that now. Hopefully it works after this.

EDIT: Still doesn't work. Just getting the same error as before. Firewall is turned off and I've completely uninstalled my antivirus - still doesn't work.